Abstract : The numerical model of Williams et al. (1992) is used to study frontogenesis from unbalanced initial conditions. The dependent variables are assumed to be independent of y. The hydrostatic Boussinesq primitive equations are used with no diffusion of heat or momentum. The model is bounded at the top and bottom by rigid planes. Periodic boundary conditions are used in the horizontal. The lateral boundaries are placed far enough from the imbalance region to avoid wave reflection. The atmosphere is assumed to have constant vertical temperature stratification. The initial imbalance is obtained by allowing a horizontal temperature gradient to exist while the initial wind is zero. In a stable stratified atmosphere, gravity waves are excited and propagate away from the imbalance region, provided no reflection occurs in the lateral boundaries. Therefore, the atmosphere tends toward a geostrophic balance away from vertical boundaries. Near these boundaries, the temperature gradient oscillates or it collapses into a front, depending on the initial Rossby (Ro) and Froude (F) numbers. A relationship between Ro and F is established which separates situations where a front may or may not form. Numerical solutions show the formation of a front within a finite period of time that tilts toward the cold air.